Я обычно работаю с массивами:

Sub Test1()

Dim rngnumbers    As Excel.Range

Dim arrVals       As variant 

Dim lngRow        As long

Arrvals = Sheet2.Range("C2:F999").value

    For Lngrow = lbound(arrvals,1) to ubound(arrvals,1)
        If arrvals(lngrow,4) >= 100 Then
                If arrvals(lngrow,1)= "John" Or arrvals(lngrow,1) = "Tom" Then '''The problem here is that it only looks at the cell C2 and not the adjacent cell
                    Sheet1.Range("I999").End(xlUp).Offset(1, 0).Value = arrvals(lngrow,4)
                Else
                End If
        End If
    Next lngrow 

End Sub

На самом деле, я бы тоже, вероятно, построил выходной массив, но мой большой палец устал ...

Два If в цикле

Версия Union

Option Explicit

Sub Test1()

    Const cFirst As Integer = 2
    Const cLast As Integer = 999
    Const cCol1 As Variant = "F"
    Const cCol2 As Variant = "C"
    Const cCol3 As Variant = "I"

    Dim i As Integer
    Dim rngU As Range

    With Sheet2
        For i = cFirst To cLast
            If IsNumeric(.Cells(i, cCol1)) And .Cells(i, cCol1) >= 100 Then
                If .Cells(i, cCol2) = "John" _
                        Or .Cells(i, cCol2) = "Tom" Then
                    If Not rngU Is Nothing Then
                        Set rngU = Union(rngU, .Cells(i, cCol1))
                      Else
                        Set rngU = .Cells(i, cCol1)
                    End If
                End If
            End If
        Next
    End With

    If Not rngU Is Nothing Then
        rngU.Copy Sheet1.Cells(cLast, cCol3).End(xlUp).Offset(1, 0)
        Set rngU = Nothing
    End If

End Sub

Вы хотите что-то подобное?

Sub Test1()

        Dim lRow As Long, r As Long
        lRow = 1000 'last row in your data
        Dim ws As Worksheet
        Set ws = Worksheets("List with your data")

        For i = 2 To lRow
            If ws.Range("F" & i) > 100 Then
                If ws.Range("C" & i).Value = "John" Or ws.Range("C" & i).Value = "Tom" Then
                    Worksheets("Another sheet sheet").Range("A" & r) = Range("C" & i).Value ' r - Row, where we want to enter uor text
                    r = r + 1 'if you want to put next name on the next row
                End If
            End If
        Next

    End Sub

Решает ли это вашу проблему - ссылка на соответствующую ячейку в столбце C? OFFSET обеспечивает относительную ссылку, в этом случае посмотрите 3 столбца слева от F.

Sub Test1()

Dim rngnumbers As Range, rngnames As Range, MultipleRange As Range, numb As Range

Set rngnumbers = Sheet2.Range("F2:F999")
Set rngnames = Sheet2.Range("C2:C999")
Set MultipleRange = Union(rngnumbers, rngnames)

For Each numb In rngnumbers
    If numb.Value >= 100 Then
        If numb.Offset(, -3) = "John" Or numb.Offset(, -3) = "Tom" Then
            Sheet1.Range("I999").End(xlUp).Offset(1, 0).Value = numb.Value
        End If
    End If
Next numb

End Sub

Вы рассматривали SUMIFS вместо этого?